Epco, Zanu, Ritux for R/R FL or MZL

Inclusion Criteria: * Histologically confirmed diagnosis of CD20+ FL (grade 1-3A) or CD20+ MZL (any subtype) (at time of trial entry) with review of the diagnostic pathology specimen at one of the participating institutions. Patients with current histologic transformation are excluded. * Receipt of at least one prior line of therapy for FL or MZL (with prior treatment including a CD20 monoclonal antibody). * Measurable disease, defined as ≥1 measurable nodal lesion (long axis \>1.5 cm or short axis \>1.0 cm), or ≥1 measurable extra-nodal lesion (long axis \>1.0 cm), or spleen \>13 cm on PET, CT, or magnetic resonance imaging (MRI). For patients with FL, disease should be FDG-avid based on PET. FDG-avid disease is NOT a requirement for patients with MZL. * Meets at least one criterion to begin treatment based on the modified GELF (Groupe d'Etude des Lymphomes Folliculaires) criteria: * Symptomatic adenopathy * Organ function impairment due to disease involvement, including cytopenias due to marrow involvement (WBC \<1.5x109/L; absolute neutrophil count \[ANC\] \<1.0x109/L, Hgb \<10g/dL; or platelets \<100x109/L) * Constitutional symptoms (defined as persistent fevers \>100.4 F, shaking chills, drenching night sweats, or loss of \>10% of body weight within 6 months) * Any nodal or extranodal tumor mass \>7 cm in maximum diameter * \>3 nodal sites of involvement \>3 cm * Local compressive symptoms or imminent risk thereof * Splenomegaly (craniocaudal diameter \> 16cm on CT imaging) * Clinically significant pleural or peritoneal effusion * Leukemic phase (\>5x109/L circulating malignant cells) * Rapid generalized disease progression * Renal infiltration * Bone lesions * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2. (Appendix A) * Age ≥18 years. * Adequate hematologic and organ function: 1. Absolute neutrophil count \> 1.0x109/L unless due to marrow involvement by lymphoma in which case ANC must be \>0.5x109/L 2. Platelets \> 75 x109/L, unless due to marrow involvement by lymphoma, in which case platelets must be \>50 x109/L 3. Estimated CrCl (based on Cockcroft Gault or MDRD) ≥ 45ml/min or ≥ 45ml/min/1.73m2 4. Total bilirubin \< 1.5 X ULN, unless Gilbert syndrome, in which case direct bilirubin must be \< 1.5 x ULN 5. AST/ALT \< 2.5 X ULN, unless documented liver involvement by lymphoma, in which case AST/ALT must be \<5 x ULN * Ability to understand and the willingness to sign a written informed consent document. * Willingness to provide a pre-treatment tumor sample by core needle or excisional surgical biopsy. A fresh biopsy is strongly encouraged, but an archival sample is acceptable if it is collected within 90 days and without intervening treatment and the following provisions are met: 1) availability of a tumor-containing formalin-fixed, paraffin-embedded (FFPE) tissue block, 2) if the tumor containing FFPE tissue block cannot be provided in total, sections from this block should be provided that are freshly cut and mounted on positively-charged glass slides. Preferably, 25 slides should be provided; if not possible, a minimum of 15 slides is required. Exceptions to this criterion may be made with approval of the Sponsor-Investigator. * Willingness to remain abstinent (1) or to use two effective contraceptive methods that result in a failure rate of \<1% per year from screening until: (a) at least 12 months after pre-treatment with rituximab, 12 months after the last dose of epcoritamab, or 3 months after the last dose of zanubrutinib, whichever is longer, if the patient is a male or (b) until at least 12 months after pre-treatment with rituximab, 12 months after the last dose of epcoritamab, or 3 months after the last dose of zanubrutinib, whichever is longer, if patient is a female. Examples of contraceptive methods with a failure rate of \<1% per year include: * Tubal ligation, male sterilization, hormonal implants, established proper use of hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices. * Alternatively, two methods (e.g., two barrier methods such as a condom and a cervical cap) may be combined to achieve a failure rate of \<1% per year. Barrier methods must always be supplemented with the use of a spermicide. 1. True abstinence is acceptable when this is in line with the preferred and usual lifestyle of the subject. In contrast, periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception. Exclusion Criteria: * Patients who require systemic immunosuppressive therapy for an ongoing medical condition will be excluded. For corticosteroids, patients receiving a prednisone dose of \>10 mg daily (or equivalent) will not be eligible. A short course of steroids (up to 14 days) for lymphoma-related symptom palliation or for prophylaxis (i.e., IV contrast allergy) is allowed, in which case patients should be off steroids prior to treatment start. * Patients with bulky cervical adenopathy that is compressing the upper airway or could result in significant airway compression during a tumor flare event. * Patients, who have had a major surgery or significant traumatic injury within 4 weeks of start of study drug, patients who have not recovered from the side effects of any major surgery (defined as requiring general anesthesia). * Presence of HCV antibody. Patients with presence of HCV antibody are eligible if HCV RNA is undetectable (NOTE: the limit of detection for HCV RNA must have a sensitivity of \< 15 IU/mL). Subjects who received treatment for HCV that was intended to eradicate the virus and who have an undetectable HCV RNA may participate without serial HCV RNA screening. Other patients may participate if they are willing to undergo every 3-month monitoring for HCV reactivation. * Presence of hepatitis B surface antigen (HBsAg) or hepatitis B core antibody (HBcAb). Patients with positive hepatitis B serologies with undetectable HBV DNA (NOTE: the limit of detection for HBV DNA must have a sensitivity of \< 20 IU/mL) are permitted in the trial but should receive prophylactic antiviral therapy (i.e. entecavir) and undergo every 3 month HBV DNA monitoring. * Known active bacterial, viral, fungal, mycobacterial, parasitic, or other infection (excluding fungal infections of nail beds) requiring antimicrobial therapy at trial enrolment or significant infections within 2 weeks of study treatment initiation. * Subject has a known active severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection. If a subject has signs/symptoms suggestive of SARS-CoV-2 infection or has had recent known exposure to someone with SARS-CoV-2 infection, the subject must have a negative molecular (e.g., PCR) test, or 2 negative antigen test results at least 24 hours apart, to rule out SARS-CoV-2 infection. Subjects who do not meet SARS-CoV-2 infection eligibility criteria must be screen failed and may only rescreen after they meet the following SARS-CoV-2 infection viral clearance criteria: * No signs/symptoms suggestive of active SARS-CoV-2 infection * Negative molecular (e.g., PCR) result or 2 negative antigen test results at least 24 hours apart * Prior history of another malignancy (except for non-melanoma skin cancer, in situ cervical or breast cancer, or Gleason 6 prostate cancer managed with observation) unless disease free for at least 2 years OR unless the likelihood of relapse is very low in the opinion of the treating physician. * Patients should not have received immunization with attenuated live vaccine within one week of study entry or during study period. Vaccination with live vaccines within 28 days of the first dose of study treatment is prohibited. * Patients who have any severe and/or uncontrolled medical conditions or other conditions that could affect their participation in the study or limit adherence to study requirements. * Patients with any one of the following currently on or in the previous 6 months will be excluded: myocardial infarction, congenital long QT syndrome, torsade de pointes, unstable angina, coronary/peripheral artery bypass graft, cardiac arrhythmia (CTCAE grade 3 or higher), or cerebrovascular accident. History of Mobitz II second-degree or third-degree heart block without a permanent pacemaker in place. Uncontrolled hypertension as indicated by ≥ 2 consecutive blood pressure measurements showing systolic blood pressure \> 170 mm Hg and diastolic blood pressure \> 105 mm Hg at screening. * Patients with 1) New York Heart Association Class III or IV heart failure or known ejection fraction of \<45%, 2) MI within 6 months prior to screening, 3) unstable angina within 3 months before screening, or 4) history of clinically significant arrhythmias within 6 months of screening (eg sustained Vtach, Vfib, torsades de pointes). * Inability to comply with protocol mandated restrictions. * Patients who are pregnant, breast-feeding, or intending to become pregnant during the study. * Prior solid organ or allogeneic stem cell transplantation. * History of known or suspected hemophagocytic lymphohistiocytosis (HLH). * History of clinically significant autoimmune disease, including but not limited to myocarditis, pneumonitis, myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjögren's syndrome, Guillain-Barré syndrome, multiple sclerosis, vasculitis, or glomerulonephritis. • Patients with a remote history of, or well controlled, autoimmune disease who meet above criteria may be eligible to enroll after consultation with the Sponsor-Investigator. * Inability to tolerate anti-CD20 mAb therapy or known allergy or intolerance to any component or excipient of epcoritamab. * Known central nervous system involvement * Neuropathy \> grade 1(based on CTCAE grading) * Treatment with CAR-T therapy within 100 days prior to first dose of epcoritamab. * Treatment with an investigational drug within 4 weeks prior to the first dose of study treatment. * Chemotherapy and other non-investigational anti-neoplastic agents (except CD20 mAbs) within 4 weeks prior to the first dose of study treatment. * Participants who require warfarin or other vitamin K antagonists for anticoagulation. Other anticoagulants including direct oral anticoagulants (i.e. apixaban, rivaroxaban) and low-molecular weight heparin are allowed. * Participants who are known at the time of study entry to require concomitant treatment with any medications or substances that are strong CYP3A inducers. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently updated medical reference. As part of the enrollment/informed consent procedures, the participant will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the participant is considering a new over-the-counter medicine or herbal product. * Unable to swallow capsules or disease significantly affecting gastrointestinal function, such as malabsorption syndrome. * History of severe bleeding disorder such as hemophilia A, hemophilia B, von Willebrand disease, or history of spontaneous bleeding requiring blood transfusions or other medical interventions. Requires ongoing treatment with warfarin or warfarin derivatives. * Prior exposure to a BTK inhibitor * A limited number of patients with BsAb-refractory disease will be permitted to enroll in each cohort (see section 2.5.3). After this limit is reached, patients with BsAb-refractory disease will be excluded. BsAb-refractory disease will be defined as failing to achieve an objective response to a prior CD3xCD20 BsAb or relapse/progression within 6 months of last dose of CD3xCD20 BsAb. * Screening 12-lead ECG showing a baseline QTcF (Fridericia's correction) \> 480 msec. * History of stroke or intracranial hemorrhage within 6 months before first dose of study drug. * Major surgery ≤ 4 weeks before the first dose of study treatment or planned during study.